Design and Validation of Methods Searching forRisk Factors in Genotype Case-Control Studies

Dumitru BrinzaAlexander Zelikovsky

Department of Computer ScienceGeorgia State University

SNPHAP 2007, January 27, 2007

Outline

SNPs, Haplotypes and Genotypes Heritable Common Complex Diseases Disease Association Search in Case-Control Studies Addressing Challenges in DA Risk Factor Validation for Reproducibility Atomic risk factors/Multi-SNP Combinations Maximum Odds Ratio Atomic RF Approximate vs Exhaustive Searches Datasets/Results Conclusions / Related & Future Work

SNP, Haplotypes, Genotypes

Human Genome – all the genetic material in the chromosomes, length 3×109 base pairs

Difference between any two people occur in 0.1% of genome

SNP – single nucleotide polymorphism site where two or more different nucleotides occur in a large percentage of population.

Diploid – two different copies of each chromosome

Haplotype – description of a single copy (expensive)

example: 00110101 (0 is for major, 1 is for minor allele)

Genotype – description of the mixed two copies

example: 01122110 (0=00, 1=11, 2=01)

Heritable Common Complex Diseases

Complex disease Interaction of multiple genes

One mutation does not cause disease Breakage of all compensatory pathways cause disease Hard to analyze - 2-gene interaction analysis for a genome-

wide scan with 1 million SNPs has 1012 pair wise tests Multiple independent causes

There are different causes and each of these causes can be result of interaction of several genes

Each cause explains certain percentage of cases

Common diseases are Complex: > 0.1%. In NY city, 12% of the population has Type 2 Diabetes

DA Search in Case/Control Study

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Disease Status

Case genotypes:

Control genotypes:

SNPs

Find: risk factors (RF) with significantly high odds ratio

i.e., pattern/dihaplotype significantly more frequent among cases than among controls

Given: a population of n genotypes each containing values of m SNPs and disease status

Challenges in Disease Association

Computational Interaction of multiple genes/SNP’s

Too many possibilities – obviously intractableMultiple independent causes

Each RF may explain only small portion of case-control study

Statistical/Reproducing Search space / number of possible RF’s

Adjust to multiple testing Searching engine complexity

Adjust to multiple methods / search complexity

Addressing Challenges in DA

Computational Constraint model / reduce search space

Negative effect = may miss “true” RF’s Heuristic search

Look for “easy to find” RF’s May miss only “maliciously hidden” true RF

Statistical/Reproducing Validate on different case-control study

That’s obvious but expensive Cross-validate in the same study

Usual method for prediction validation

Significance of Risk Factors

Relative risk (RR) – cohort study

Odds ratio (OR) – case-control study

P-value binomial distribution

Searching for risk factors among many SNPs requires multiple testing adjustment of the p-value

Reproducibility Control

Multiple-testing adjustment Bonferroni

easy to compute overly conservative

Randomization computationally expensive more accurate

Validation rate using Cross-Validation Leave-One-Out Leave-Many-Out Leave-Half-Out

Atomic Risk Factors, MSCs and Clusters

Genotype SNP = Boolean function over 2 haplotype SNPs 0 iff g0 = (x NOR y) is TRUE

1 iff g1 = (x AND y) is TRUE

2 iff g2 = (x XOR y) is TRUE

Single-SNP risk factor = Boolean formula over g0, g1 and g2

Complex risk factor (RF) = CNF over single-SNP RF’s:

g01 (g0+ g2)2 (g1+ g2)3 g0

5 Atomic risk factor (ARF) = unsplittable complex RF’s:

g01 g2

2 g13 g0

5 single disease-associated factor

ARF ↔ multi-SNP combination (MSC) MSC = subset of SNP with fixed values of SNPs, 0, 1, or 2

Cluster= subset of genotypes with the same MSC

MORARF formulation

Maximum Odds Ratio Atomic Risk Factor

Given: genotype case-control study Find: ARF with the maximum odds ratio

Clusters with less controls have higher OR=> MORARF includes finding of max control-free cluster

MORARF contains max independent set problem => No provably good search for general case-control study

Case-control studies do not bother to hide true RF=> Even simple heuristics may work

Requirements to Approximate search

Fast longer search needs more adjustment

Non-trivial exhaustive search is slow

Simple Occam’s razor

Exhaustive Searching Approaches Exhaustive search (ES)

For n genotypes with m SNPs there are O(nkm) k-SNP MSCs

Exhaustive Combinatorial Search (CS) Drop small (insignificant) clusters Search only plausible/maximal MSC’s

Case-closure of MSC: MSC extended with common SNPs values in all cases Minimum cluster with the same set of cases

0 1 1 0 1 2 0 0 2 control

0 1 1 0 1 2 1 0 2 case 2 0 1 1 0 2 0 0 1 case 0 0 1 0 0 0 0 2 1 case 0 1 1 0 1 2 0 0 2 control

x x 1 x x 2 x x xPresent in 2 cases : 2 controls

Case-closure

0 2 1 0 1 2 0 1 2 control

0 1 1 0 1 2 1 0 2 case 2 0 1 1 0 2 0 0 1 case 0 0 1 0 0 0 0 2 1 case 0 1 1 0 1 2 0 0 2 control

x x 1 x x 2 x 0 x

Present in 2 cases : 1 control

i i

Combinatorial Search

Combinatorial Search Method (CS):

Searches only among case-closed MSCs Avoids checking of clusters with small number of

cases Finds significant MSCs faster than ES Still too slow for large data Further speedup by reducing number of SNPs

Complimentary Greedy Search (CGS) Intuition:

Max OR when no controls – chosen cases do not have simila

Max independent set by removing highest degree vertices Fixing an SNP-value

Removes controls -> profit Removes cases -> expense

Maximize profit/expense! Algorithm:

Starting with empty MSC add SNP-value removing from current cluster max # controls per case

Extremely fast but inaccurate, trapped in local maximum

Cases Controls

Disease Association Search

AcS – alternating combinatorial search method

RCGS – Randomized complimentary greedy search method

5 Data Sets

Crohn's disease (Daly et al ): inflammatory bowel disease (IBD). Location: 5q31 Number of SNPs: 103 Population Size: 387 case: 144 control: 243 Autoimmune disorders (Ueda et al) : Location: containing gene CD28, CTLA4 and ICONS Number of SNPs: 108 Population Size: 1024 case: 378 control: 646 Tick-borne encephalitis (Barkash et al) : Location: containing gene TLR3, PKR, OAS1, OAS2, and OAS3. Number of SNPs: 41 Population Size: 75 case: 21 control: 54 Lung cancer (Dragani et al) : Number of SNPs: 141 Population Size: 500 case: 260 control: 240 Rheumatoid Arthritis (GAW15) : Number of SNPs: 2300 Population Size: 920 case: 460 control: 460

Search Results

Validation Results

Conclusions

Approximate search methods find more significant RF’s

RF found by approximate searches have higher cross-validation rate Significant MSC’s are better cross-validated

Significant MSC’s with many SNPs (>10) can be efficiently found and confirmed

RCGS (randomized methods) is better than CGS (deterministic methods)

Related & Future Work

More randomized methods Simulated Annealing/Gibbs Sampler/HMM But they are slower

Indexing (have our MLR tagging) Find MSCs in samples reduced to index/tag SNPs May have more power (?)

Disease Susceptibility Prediction Use found RF for prediction rather prediction for RF search